As others have said, it isn’t an MPG vs MP4 issue, it is a file size/network transfer issue. if you made MPG files the same size as the MP4 files, i bet you would not have a problem
Over-the-air HD in the US is about 18 Mbps, per channel after overhead, and with most channels dividing this among 1-2 sub-channels, the actual bandwidth of and individual recording is less. I first started recording MPEG-2 on ATA-100 drives almost a decade ago. You have some type of hardware or networking limitation.
if you are on a 1000 Mbps ethernet network, 18 Mbps will barely be a blip.
if you are on a wireless then you have to worry about latency & all sorts of issues that will affect the streaming higher bandwidth video.
Automatic transcoding is a dire necessity. This was one of my first draws to SageTV back in '08/'09 when ATSC first was rolling out in the US. Video is already transcoded for iOS, etc, so i do not understand the delay in transcode & replace…
EDIT
personally, i stream, over 802.11/n, ATSC MPEG-2 recordings everyday & have no issues with playback at all.